Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Automatic differentiability and characterization of cocycles of holomorphic flows

Author(s): Farhad Jafari; Thomas Tonev; Elena Toneva
Journal: Proc. Amer. Math. Soc. 133 (2005), 3389-3394.
MSC (2000): Primary 47D03; Secondary 47B38
Posted: June 7, 2005
MathSciNet review: 2161164
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Abstract | References | Similar articles | Additional information

Abstract: In this paper we prove that cocycles of holomorphic flows on domains in the complex plane are automatically differentiable with respect to the flow parameter, and their derivatives are holomorphic functions. We use this result to show that, on simply connected domains, an additive cocycle is a coboundary if and only if this cocycle vanishes at the fixed point of the flow.

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